reserve x,y,z,x1,x2,x3,x4,y1,y2,s for Variable,
  M for non empty set,
  a,b for set,
  i,j,k for Element of NAT,
  m,m1,m2,m3,m4 for Element of M,
  H,H1,H2 for ZF-formula,
  v,v9,v1,v2 for Function of VAR,M;

theorem Th5:
  not x in variables_in H implies (M,v |= H iff M,v/(x,m) |= H)
proof
A1: M,v/(x,m) |= All(x,H) implies M,(v/(x,m))/(x,v.x) |= H by ZF_LANG1:71;
A2: (v/(x,m))/(x,v.x) = v/(x,v.x) by FUNCT_7:34;
  M,v |= All(x,H) implies M,v/(x,m) |= H by ZF_LANG1:71;
  hence thesis by A1,A2,Th4,FUNCT_7:35;
end;
